Here are three general phases in befriending the shadow, letting go of narrow identities, or inquiring into beliefs (all aspects of the same process)...

Being blindly in the grips of it, not even noticing what is going on

Noticing it as a shadow, an identity, a belief, and exploring it

Finding resolution through befriending and becoming intimately familiar with it, and seeing what was already more true for me than my surface belief

During the second phase, when it is still half-resolved, I notice in myself and others a tendency to begrudgingly accept it. I know, on an idea level and from past experience, that it is a shadow and comes from a belief, but am still in the grips of it on an emotional level, and to some extent also on a behavioral level (it seeps out, even if I try to hold it back.)

I know there is a monster in the back yard, and that I cannot get rid of it, but I am not happy about it either.

Genuine appreciation

Exploring it further, more wholeheartedly, in my daily life and in more detail, seeing what is already more true for me, the monster is revealed as not a monster at all. I find the genuine gifts in that which was placed in the shadow, and in the situation I initially didn't want.

As in the story of Jim Button and Luke the Engine Driver by Michael Ende, the demonic queen dragon turned into, when captured and kept safely in a cage, a golden dragon of wisdom. The horrors of it was real as long as it was roaming free, untamed by civilization. But through capturing it, and containing it without killing it, it was allowed to transform into golden wisdom.

What I initially was blind to, and then begrudgingly accepted, is now something there is genuine and unreserved appreciation for.

Examples

For instance, say I have a chronic illness. Initially, I am identified with getting rid of it. After a while, seeing that it hasn't worked yet, I start working on my own attitudes around it. I try to find peace with it, although I still see the illness as something awful and undesirable. Eventually, I may come to see the real gifts in the illness... I start realize what it has brought to my life that I genuinely appreciate... the maturing and deepening that has happened for me through the illness... this obstacle which nothing could be done with... I may still not have chosen it, if there had been a choice, but now, there is a genuine appreciation for it. Beyond acceptance, is appreciation.

Or I may have trouble with anger, for instance through a one-sided identity as somebody who is not angry. Anger then becomes a real problem, and something I try to avoid in myself and others. It becomes a monster in my life. Then, I may half-heartedly accept that it is here as well, although I still don't like it much. And finally, as I explore it further, I see how it supports my life when it is allowed to become a part of the team of all of me. I learn to genuinely appreciate all of its many gifts to my life... its energy, its ability to get things done in certain situations, its assistance in getting through to people if everything else fails.

Alchemy

In alchemy, this is the process of nigredo (the suffering of being in the grips of it), albedo (the work), and rubedo (the fruition of the work.)